Temperature-dependent Elastic Properties Research Articles

Estimating equivalent elastic properties of frozen clay soils using an XFEM-based computational homogenization

This study addresses the challenge of estimating the elastic properties of heterogeneous frozen clay soils by introducing a comprehensive approach that combines analytical and numerical models. The frozen clay soil is treated as a mixture composed of frozen clay-water composites and nonclay mineral inclusions. An inversion algorithm is employed to deduce the elastic properties of the matrix (clay-water composites) of two artificially frozen sandy clay samples with known temperature-dependent elastic properties. Subsequently, a two-dimensional numerical simulation using the eXtended Finite Element Method (XFEM) is conducted to carry out numerical homogenization by considering the imperfect bond among frozen clay-water composites and nonclay minerals. The numerical homogenization model offers insights into the temperature-dependent behavior of the interface stiffness parameter. The numerical homogenization results are compared with conventional numerical homogenization approaches like the FEM, which rigidly defines the bonding between inclusions and the matrix. The comparison indicates that the neglect of imperfect bonds among clay-water composites and nonclay minerals will lead to unrealistic outcomes in cases with a high fraction of inclusions. This integrated approach advances the understanding and prediction of elastic properties of frozen clay soils by considering their heterogeneous nature.

Flexoelectric Enhancement of Strain Gradient Elasticity Across a Ferroelectric-to-Paraelectric Phase Transition.

We study the temperature dependent elastic properties of Ba0.8Sr0.2TiO3 freestanding membranes across the ferroelectric-to-paraelectric phase transition using an atomic force microscope. The bending rigidity of thin membranes can be stiffer compared to stretching due to strain gradient elasticity (SGE). We measure the Young's modulus of freestanding Ba0.8Sr0.2TiO3 drumheads in bending and stretching dominated deformation regimes on a variable temperature platform, finding a peak in the difference between the two Young's moduli obtained at the phase transition. This demonstrates a dependence of SGE on the dielectric properties of a material and alludes to a flexoelectric origin of an effective SGE.

Combined thermal and particle shape effects on powder spreading in additive manufacturing via discrete element simulations

The thermal and mechanical behaviors of powders are crucial for additive manufacturing. In powder bed fusion, capturing temperature profiles and packing structures before melting is challenging due to diverse heat transfer pathways and powder properties. This study tackles this challenge with a discrete element model simulating non-spherical particles with thermal properties during powder spreading. Thermal conduction and radiation are integrated into a multisphere particle formulation to model heat transfer among irregular-shaped powders with temperature-dependent elastic properties. The model is utilized to simulate the spreading of pre-heated PA12 powder over a hot substrate representing the part under manufacturing. Variances in temperature profiles are observed in the spreading cases based on particle shapes, spreading speed, and temperature-dependent elastic modulus. Particle temperature beneath the spreading blade is influenced by the kinematics of the particle heap and temperature-dependent properties.

Analyze the temperature-dependent elastic properties of single-walled boron nitride nanotubes by a modified energy method

The elastic properties of boron nitride nanotubes (BNNTs) were investigated utilizing an enhanced energy method. By considering small deformations and applying the principle of minimum potential energy, the variations in atomic bonds and bond angles within the nanotube structure were determined. The modified model incorporated the contribution of inversion energy to the overall potential energy of the system, leading to the derivation of analytical expressions for the Young's modulus, shear modulus, and strain energy of both armchair and zigzag BNNTs under varying temperatures. The results indicate that compared to zigzag BNNTs, the impact of inversion energy on the elastic constants of armchair BNNTs is more significant, especially at small diameters (<1 nm). In thermal environment, this study demonstrates that the change in Young's modulus of BNNTs is lower than that of carbon nanotubes (CNTs), confirming the superior thermal stability of BNNTs over CNTs. Furthermore, molecular structure mechanics (MSM) and continuum mechanics models were employed to analyze the strain energy of BNNTs. The effects of different bonds, bond angles, and inversion angles on strain energy were analyzed in a thermal environment, revealing distinct differences between the two types of BNNTs. These findings provide more accurate theoretical guidance for thermal applications based on the stretching of BNNTs.

Temperature-dependent characterization of full tensor properties of [111]c poled Mn-doped 28PIN-43PMN-29PT single crystals

The temperature-dependent characterization of full tensor properties of single-domain relaxor-based single crystals (SCs) is important for understanding the influence of temperature on the properties of their multidomain SCs. However, no relevant results have been published because characterization is difficult to achieve using the traditional electric resonance method. In this Letter, the temperature-dependent elastic and piezoelectric properties of single-domain [111]c poled Mn-doped 28Pb(In1/2Nb1/2)O3-43Pb(Mg1/3Nb2/3)O3-29PbTiO3 SCs were investigated in the range of 20–80 °C by resonant ultrasound spectroscopy (RUS) using a rectangular parallelepiped sample. The temperature-dependent dielectric constants were calculated from the measured capacitances of the sample. The results are self-consistent because they were obtained from the same sample. The elastic constants obtained using the ultrasonic pulse-echo method agree closely with those obtained using RUS. Moreover, the experimental results of electric impedance spectrum agree closely with those simulated using the material constants characterized herein, indicating that the characterization is reliable.

Molecular dynamics exploration of the temperature-dependent elastic, mechanical, and anisotropic properties of hcp ruthenium

Molecular dynamics calculations were performed for the hitherto unclarified temperature-dependent elastic, mechanical, and anisotropic properties of the hexagonal closed pack (hcp) ruthenium (Ru) between 0 and 1200 K. All elastic stiffness constants were found to decrease with increasing temperature. Under the examined temperature range, hcp Ru obeys Born stability conditions. Further, both Pugh ratio analyses and calculated Poisson ratio values mutually suggest the brittle character of hcp Ru between 0 and 1200 K. The intricate hardness behavior of hcp Ru was also obtained and discussed throughout the work. For the considered temperature range, hcp Ru exhibits apparent elastic anisotropy that exponentially increases with increasing temperature. Moreover, presently obtained ground state (T = 0 K and P = 0 GPa) theoretical data for hcp Ru agree well with the former experimental and theoretical data. The present findings on the temperature-dependent characteristics of this metal may further inspire future applied works.Graphical abstract

Temperature-Dependent Structural and Elastic Properties of CdS, CdSe, and CdTe Compounds Studied by Statistical Moment Method

The statistical moment method has been applied to investigate the temperature effects on the lattice parameters and elastic properties of the zinc-blende CdX (X = S, Se, Te) compounds. The analytical expressions of thermal-induced atomic displacement, lattice constant, elastic moduli (Young’s modulus, bulk modulus and shear modulus) and elastic constants (including C11,C12 and C44) of the zinc-blende compounds have been derived. We have pointed out that the temperature effects on the elastic properties of CdS and CdSe are almost the same. And the elastic quantities of CdS and CdSe are more strongly dependent on temperature than those of CdTe semiconductor. This phenomenon is caused by the weaker coupling force of Cd-Te bonds compared to those of Cd-S and Cd-Se bonds. Furthermore, from the calculated Debye temperatures of CdX (X = S, Se, Te) compounds we conclude that CdS has higher phonon thermal conductivity and is therefore more thermally conductive among the three semiconductor compounds. The calculations of present work can be used as an appropriate reference for the experiments in future.

Temperature-Dependent Elastic Properties of B4C from First-Principles Calculations and Phonon Modeling

Boron carbide plays a crucial role in various extreme environment applications, including thermal barrier coatings, aerospace applications, and neutron absorbers, because of its high thermal and chemical stability. In this study, the temperature-dependent elastic stiffness constants, thermal expansion coefficient, Helmholtz free energy, entropy, and heat capacity at a constant volume (Cv) of rhombohedral B4C have been predicted using a quasi-harmonic approach. A combination of volume-dependent first-principles calculations (density functional theory) and first-principles phonon calculations in the supercell framework has been performed. Good agreement between the elastic constants and structural parameters from static calculations is observed. The calculated thermodynamic properties from phonon calculations show trends that align with the literature. As the temperature rises, the predicted free energy follows a decreasing trend, while entropy and Cv follow increasing trends with temperature. Comparisons between the predicted room temperature thermal expansion coefficient (TEC) (7.54×10−6 K−1) and bulk modulus (228 GPa) from the quasi-harmonic approach and literature results from experiments and models are performed, revealing that the calculated TEC and bulk modulus fall within the established range from the limited set of data from the literature (TEC = 5.73–9.50 ×10−6 K−1, B = 221–246 GPa). Temperature-dependent Cijs are predicted, enabling stress analysis at elevated temperatures. Overall, the outcomes of this study can be used when performing mechanical and thermal stress analysis (e.g., space shielding applications) and optimizing the design of boron carbide materials for elevated temperature applications.

Modeling temperature-dependent 2D phase behavior and elastic properties of lung surfactant monolayers at air-water interfaces using dissipative particle dynamics simulations

Modeling temperature-dependent 2D phase behavior and elastic properties of lung surfactant monolayers at air-water interfaces using dissipative particle dynamics simulations

Influence of temperature on the elastic properties of graphene and graphene-like nanosheets based on the asymptotic homogenization method

In this paper, the effective elastic properties of hexagonal monolayers such as graphene, boron nitride, silicon carbide, and aluminum nitride are evaluated using the asymptotic homogenization method taking into account temperature changes. The effective properties are determined analytically by considering temperature, force constants, bond lengths, and thickness, using atomic interactions within the context of the unit cell problem. The relationship between environmental temperature and the coefficient of thermal expansion is established by considering changes in the values ​​of bond stretching, bond angle bending, and torsion resistance constants at different temperatures from 0 to 1800 K. The results provided by the proposed homogeneous model are consistent with the valid findings of other researchers in the literature. It is found that these different hexagonal nanosheets exhibit isotropic temperature-dependent properties and their Young's and shear modulus decrease almost linearly as the temperature rises, considering a constant coefficient of thermal expansion. However, Poisson's ratio is found to be independent of temperature. Furthermore, the temperature-dependent elastic properties of these nanosheets become nonlinear when the variation of the coefficient of thermal expansion with temperature is taken into account. The Young and shear moduli of the nanosheets increase as the coefficient of thermal expansion decreases and vice versa. The highest elastic modulus values are obtained when the thermal expansion is close to its minimum threshold. However, it is recognized that the elastic modulus of graphene and boron nitride nanosheets is higher than that of silicon carbide and aluminum nitride at any temperature. As an alternative to lengthy computer modeling or rigorous testing, the homogeneous models provided can be used to simulate nanosheets.

Which Ion Dominates the Temperature and Pressure Response of Halide Perovskites and Elpasolites?

Halide perovskites and elpasolites are key for optoelectronic applications due to their exceptional performance and adaptability. However, understanding their crucial elastic properties for synthesis and device operation remains limited. We performed temperature- and pressure-dependent synchrotron-based powder X-ray diffraction at low pressures (ambient to 0.06 GPa) to investigate their elastic properties in their ambient-pressure crystal structure. We found common trends in bulk modulus and thermal expansivity, with an increased halide ionic radius (Cl to Br to I) resulting in greater softness, higher compressibility, and thermal expansivity in both materials. The A cation has a minor effect, and mixed-halide compositions show intermediate properties. Notably, thermal phase transitions in MAPbI3 and CsPbCl3 induced lattice softening and negative expansivity for specific crystal axes, even at temperatures far from the transition point. These results emphasize the significance of considering temperature-dependent elastic properties, which can significantly impact device stability and performance during manufacturing or temperature sweeps.

Elastic modulus data for additively and conventionally manufactured variants of Ti-6Al-4V, IN718 and AISI 316 L

This article reports temperature-dependent elastic properties (Young’s modulus, shear modulus) of three alloys measured by the dynamic resonance method. The alloys Ti-6Al-4V, Inconel IN718, and AISI 316 L were each investigated in a variant produced by an additive manufacturing processing route and by a conventional manufacturing processing route. The datasets include information on processing routes and parameters, heat treatments, grain size, specimen dimensions, and weight, as well as Young’s and shear modulus along with their measurement uncertainty. The process routes and methods are described in detail. The datasets were generated in an accredited testing lab, audited as BAM reference data, and are hosted in the open data repository Zenodo. Possible data usages include the verification of the correctness of the test setup via Young’s modulus comparison in low-cycle fatigue (LCF) or thermo-mechanical fatigue (TMF) testing campaigns, the design auf VHCF specimens and the use as input data for simulation purposes.

The influence of site preference on the elastic properties of FCC_CoCrFeNi multi-principal element alloy

The influence of the existing site preference of the constituent elements on the sublattice on elastic properties is rarely explored in multi-principal element alloys (MPEAs). In this work, in order to explore the influence of the site preference of constituent atoms on the thermodynamic properties and elastic properties, the ordered configurations based on the previously predicted site occupying fractions (SOFs) and the disordered configuration based on a special quasi-random structure (SQS) were established, and the thermodynamic properties and elastic properties were predicted using the quasi-harmonic approximation (QHA) method first. It was found that the site preferring behaviors of atoms on the sublattices will not only improve the stability of the structure but will also lead to bigger elastic properties than its ideal disordered structure. Although the prediction of the temperature-dependent elastic properties using the QHA method shortens the time costs by only considering the effects of thermal expansion, it ignores the significant effect of lattice vibration on elastic properties at high temperatures. In order to explore the influence of lattice vibration on the temperature-dependent elastic properties further, the elastic properties of the ordered FCC_CoCrFeNi MPEA were predicted using the ab initio molecular dynamics (AIMD) method at several selective temperatures. The results show that except for the elastic constant C12 and bulk modulus, the lattice vibration reduces other elastic properties on the basis of thermal expansion. The predicted temperature-dependent shear and Young's moduli agree well with the limited experimental literature data. Thus, the temperature-dependent elastic properties can be reasonably predicted using the AIMD method based on site preference. The predicted polycrystalline elastic moduli B, G, and E of FCC_CoCrFeNi MPEA at 973 K are 146.68, 53.79, and 143.78 GPa, respectively.

Three-dimensional J-integral evaluation for thermomechanically loaded cracks and temperature-dependent incremental plasticity

In this paper, the J-integral is derived for temperature-dependent elastic–plastic materials described by incremental plasticity. It is implemented using the equivalent domain integral method for assessment of three-dimensional cracks based on results of finite-element calculations. The J-integral considers contributions from inhomogeneous temperature fields and temperature-dependent elastic and plastic material properties as well as from gradients in the plastic strains and the hardening variables. Different energy densities are considered, the Helmholtz free energy and the stress-working density, providing a physical meaning of the J-integral as a fracture criteria for crack growth. Results obtained for a plate with two different crack configurations each loaded by a cool-down thermal shock show domain-independence of the incremental J-integral for different energy densities even for high temperature gradients and significant temperature-dependence of the yield stress and the hardening exponent in the presence of large scale yielding. Hence, the derived J-integral is an appropriate parameter for the assessment of cracks in thermomechanically loaded components.

Development of the RF-MEAM Interatomic Potential for the Fe-C System to Study the Temperature-Dependent Elastic Properties.

One of the major impediments to the computational investigation and design of complex alloys such as steel is the lack of effective and versatile interatomic potentials to perform large-scale calculations. In this study, we developed an RF-MEAM potential for the iron-carbon (Fe-C) system to predict the elastic properties at elevated temperatures. Several potentials were produced by fitting potential parameters to the various datasets containing forces, energies, and stress tensor data generated using density functional theory (DFT) calculations. The potentials were then evaluated using a two-step filter process. In the first step, the optimized RSME error function of the potential fitting code, MEAMfit, was used as the selection criterion. In the second step, molecular dynamics (MD) calculations were employed to calculate ground-state elastic properties of structures present in the training set of the data fitting process. The calculated single crystal and poly-crystalline elastic constants for various Fe-C structures were compared with the DFT and experimental results. The resulting best potential accurately predicted the ground state elastic properties of B1, cementite, and orthorhombic-Fe7C3 (O-Fe7C3), and also calculated the phonon spectra in good agreement with the DFT-calculated ones for cementite and O-Fe7C3. Furthermore, the potential was used to successfully predict the elastic properties of interstitial Fe-C alloys (FeC-0.2% and FeC-0.4%) and O-Fe7C3 at elevated temperatures. The results were in good agreement with the published literature. The successful prediction of elevated temperature properties of structures not included in data fitting validated the potential's ability to model elevated-temperature elastic properties.

Machine learning and molecular dynamics based models to predict the temperature dependent elastic properties of silver nanowires

Metallic nanowires are now extensively used in several nanoscale devices and applications. To further enhance their efficient usage, the estimation and prediction of thermal and mechanical properties of these nanowires is very important. Performing experimental studies on the objects of such a small dimension is quite challenging. Molecular dynamics simulation technique can easily simulate and perform virtual experimentation on the objects of nanoscale dimensions. In the present work, silver nanowires of known dimension simulated and a uniaxial stress has been implemented using the Molecular dynamics approach. The stress-strain data generated by MD simulation, has been utilized to train, test and validate different machine learning models. These machine-learning models offer a reasonably good amount of predictability of the tensile characteristics of the silver nanowire at any temperature.

Finite temperature properties of uranium mononitride

Uranium mononitride (UN) is a promising nuclear fuel that combines the advantageous properties of readily used UO2 and uranium alloys, such as high melting temperature and high uranium density, and thermal conductivity, respectively. A better understanding of UN behavior at operating temperatures can be obtained from finite temperature data, such as elastic properties. To get this information, ab initio molecular dynamics (AIMD) simulations were performed at five different temperatures using constant volume (NVT) and constant pressure (NPT) ensembles. Initially, the performance of PBE functional in reproducing experimental crystallographic properties and magnetic ordering is assessed. The finite temperature phonon dispersions are calculated using NVT simulation results, which show a softening of the phonon modes with increasing temperature. The NPT results are used to obtain the thermal expansion of UN and finite temperature electronic properties. The calculated thermal expansion is compared with our measurements using neutron diffraction. Additionally, the temperature dependent elastic properties of UN are evaluated using the strain-stress method in AIMD simulations, indicating that UN becomes softer and more compressible with increasing temperature. Also, the calculated Young’s modulus slope is in very good agreement with the experiment. The finite temperature heat capacity and electronic thermal conductivity are calculated from AIMD simulations, which are in better agreement with the experiment than the heat capacity and thermal conductivity calculated using the structures relaxed at 0 K. Lastly, the thermal diffusivity from AIMD has opposite temperature dependence compared to experimental results, which we argued comes from the underestimated electronic thermal conductivity.

Amplitude-variation-with-offset in thermoelastic media

Temperature is an important factor for evaluating the seismic response of deep reservoirs. We have developed an amplitude-variation-with-offset approximation based on the Lord-Shulman thermoelasticity theory. The model predicts two compressional (P and T) waves (the second is a thermal mode) and a shear (S) wave. The T mode is due to the coupling between the elastic and heat equations. In the thermoelastic case, the approximation is more accurate than in the elastic case. Its accuracy is verified by comparison with the exact equations calculated in terms of potential functions. We examine two reservoir models with high temperatures and compute synthetic seismograms that illustrate the reliability of the approximation. Moreover, we consider real data to build a model and find that the approximate equation not only simplifies the calculations but also is accurate enough and can be used to evaluate the temperature-dependent elastic properties, providing a basis for further application of the thermoelasticity theory, such as geothermal exploration, thermal-enhanced oil recovery, and ultradeep oil and gas resources subject to high temperatures.

Thermo-mechanical large deformation characteristics of cutout borne multilayered curved structure: Numerical prediction and experimental validation

The numerical modeling of static large-deformation behavior of the multilayered flat/curved panels with cutouts subjected to thermo-mechanical load is presented in this work. The numerical model includes third-order displacement polynomials. The large-deformation characteristic of the multilayered panel is incorporated using two nonlinear strains (Green–Lagrange and von-Karman). The governing equation is formulated using Hamilton’s principle, and approximate numerical solutions are obtained using the selective integration scheme (Gauss-Quadrature) associated with Picard’s direct iterative method. A generic computational algorithm is developed in MATLAB using isoparametric finite element (FE) steps. The solution accuracy is verified with the published results and experimental data by utilizing the available/fabricated lab-scale test rig. The role of cutout parameters, including the various geometrical parameters on the nonlinear structural responses, is studied for a clear insight into the damaged structural modeling using the temperature-dependent elastic properties of the laminate. In addition, the effect of nonlinear strain terms on the final structural responses is presented. Based on the observation, the applicability of the full geometrical (Green–Lagrange) strain–displacement relation is established.

Transient response of pre-twisted FG-GRC sandwich conical shell subjected to low-velocity impact in thermal environment

A finite element method-based dynamic analysis of pre-twisted sandwich conical shell panel having functionally graded graphene-reinforced composite (FG-GRC) facings and homogenous core without or with pores under low-velocity impact in thermal environments is performed utilizing a higher-order shear deformation theory (HSDT). In each facing, the graphene sheets are either uniformly dispersed or layer-wise functionally graded across its thickness. The extended Halpin-Tsai model is employed to estimate the temperature-dependent elastic properties of the nanocomposite facings. The contact force induced between the impactor and target panel is computed through the modified Hertzian contact law. The equations of motion of the FG-GRC sandwich conical shell panel are formulated based on Lagrange’s equation. The solutions of the resulting equations of motion are obtained employing Newmark’s time integration scheme. After verifying the consistency and accurateness of the present method, the effects of some critical parameters like graphene grading profile, temperature, core-to-facings thickness ratio, pre-twist angle, span-to-cone length ratio, impactor’s initial velocity, impactor’s size, and porosity coefficient on the impact response of the pre-twisted FG-GRC sandwich conical shell panel in uniform thermal environments are scrutinized.